I absolutely agree that kittening so close together is *very* difficult for a cat as it keeps them run-down in condition. However, spaying right now would also be harmful to the Mom-cat and detrimental to the development of her current litter.
You do not want another litter of kittens.
Litter is 6wks old and about 2-4wks away from weaning.
Momcat got out 2wks ago and would be 6wks away from parturition.
IMO, I feel this leaves you with a 4-5week window.
You have to balance this between benefit for the current litter, difficulty of spay at pregnancy-stage and stress of litter abortion for the spay-team.
IMO, I would leave this litter with momcat until they are 10wks old. They learn important cat-things during this time with their mother. Spaying her early would leave her vulnerable to infection, especially if the kitts attempt to nurse and knead her belly. Many vets won't spay nursing momcats because of this issue with infection.
4wks would give her and the kitts ample time to wean and transition to solid food, then a week of separation so her milk can begin to dry up and reduce complications of recovery after spay, though her risk will be higher for the spay itself, depending on the status of her possible pregnancy.
Can you bring her to the vet for an exam to determine if she even *is* pregnant and would require an early-spay?